Coalescence Scavenging Drives Droplet Number Concentration in Southern Ocean Low Clouds

Cloud droplet number concentration (Nd) is a key microphysical property that is largely controlled by the balance between sources and sinks of aerosols that serve as cloud condensation nuclei (CCN). Despite being a key sink of CCN, the impact of coalescence scavenging on Southern Ocean (SO) cloud is poorly known. We apply a simple source‐and‐sink budget model based on parameterizations to austral summer aircraft observations to test model behavior and examine the relative influence of processes that determine Nd in SO stratocumulus clouds. The model predicts Nd with little bias and a correlation coefficient of ∼0.7 compared with observations. Coalescence scavenging is found to be an important sink of CCN in both liquid and mixed‐phase precipitating stratocumulus and reduces the predicted Nd by as much as 90% depending on the precipitation rate. The free tropospheric aerosol source controls Nd more strongly than the surface aerosol source during austral summer.


10.1029/2022GL097819
2 of 10 particles through collision-coalescence, hereafter coalescence scavenging, has long been recognized as a leading (if not the dominant) mechanism by which aerosols are removed from the MBL (Feingold et al., 1996;Wood et al., 2012). This includes over the SO where aircraft observations have shown that aerosols that serve as CCN have lower concentrations in the BL under cloudy conditions than clear conditions (Hudson et al., 1998;Yum & Hudson, 2004).
Satellite observations show that SO low clouds have significant seasonal and latitudinal dependencies. Low clouds have higher mean N d during the austral summer than winter, as well as higher mean N d near Antarctica (south of 55-60°S) (D. T. McCoy et al., 2014;I. L. McCoy et al., 2020). Previous studies showed that the seasonal and spatial patterns of SO N d are strongly influenced by aerosol sources and coalescence scavenging. I. L. McCoy et al. (2020) hypothesized that the N d minimum off the coast of Antarctica was due to enhanced coalescence scavenging associated with the SO storm track. Using a simplifed budget model (Wood et al., 2012, hereafter W12), along with CloudSat-derived precipitation estimates, I. L. McCoy et al. (2020) found that coalescence scavenging could drive down mean N d to about 30% of the value that would occur without coalescence scavenging. However, differences in aerosol sources compete with precipitation sink patterns in explaining the latitudinal dependence. Sources contribute heavily to seasonal differences, with ocean biology-sourced aerosols dominating CCN in the summertime and sea spray dominating in the winter (Ayers & Gras, 1991;Quinn et al., 2017). Observations and model studies (e.g., Korhonen et al., 2008) suggest that surface dimethyl sulfide (DMS) emissions associated with phytoplankton can be transported from the surface to the free troposphere (FT) where DMS oxidation products nucleate into new particles (A. D. Clarke et al., 1998;Weber et al., 2001). These particles subsequently return to the MBL through entrainment and subsidence associated with mid-latitude storm systems (Covert et al., 1996) and grow into CCN (Quinn et al., 2017;Raes, 1995;Sanchez et al., 2021). I. L. McCoy et al. (2021) suggest that these FT Aitken particles (diameters ≤0.1 μm), in addition to acting as the primary source of CCN, also buffer SO CCN and N d against precipitation removal during biologically active time periods. The latitudinal pattern is driven in part by the large increases in the amount of phytoplankton and thus DMS production in the summertime seasonal ice zone around Antarctica (Curran & Jones, 2000) and increases in small aerosol particles south of the oceanic polar front during the SO summer (Humphries et al., 2016(Humphries et al., , 2021. Across the SO, strong correlations are observed between satellite retrieved N d and sea surface chlorophyll-a concentrations (a proxy for phytoplankton biomass; D. T. McCoy et al., 2015). Summertime MBL accumulation mode aerosols (include most CCN) observed during the recent SO Clouds Radiation Aerosol Transport Experimental Study (SOCRATES;McFarquhar et al., 2021) were dominated by sulfur-based particles (∼70% by number) which likely had a biogenic origin. Sea-spray particles also contributed to the total (∼30% by number) but many of these particles (40%) were still influenced by ocean biology as their compositions were salt enriched by sulfur and depleted in chlorine through uptake and condensation of sulfur gases .
There is little doubt that aerosols from biological sources play a large role in both the seasonal and latitudinal variations in SO low cloud N d . However, coalescence scavenging has a non-trivial influence in determining the pattern of N d across the SO and its influence over the SO remains poorly understood. In this study, we examine this through a N d budget model framework. We first test the ability of the W12 budget model to predict N d for SO stratocumulus using SOCRATES observations. This model was developed in the context of observations gathered in subtropical stratocumulus and has been applied in other subtropical settings (Mohrmann et al., 2018;Zheng et al., 2018). While it was applied by I. L. McCoy et al. (2020) to the SO, it has not been tested in any detail at mid-to-high latitudes of either hemisphere. We find that the model (after being adjusted to better represent SO sea spray aerosols) can predict much of the observed N d variability (Section 3.1). This model skill is apparent in both regimes of liquid and mixed-phase precipitation (Section 3.2), suggesting coalescence scavenging is a dominant sink for CCN. We then use the model to examine the relative importance of FT and surface sources of CCN and, to assess the importance of coalescence scavenging in controlling SO stratocumulus N d (Section 3.3).

Data and Methods
To quantitatively study the sources and sinks that control N d , we apply a budget model, developed by W12, that considers the main sources and sinks of CCN and thus N d : The terms on the right-hand side refer to the time tendency of CCN due to entrainment from the FT, primary production at the sea surface from sea-spray, new particle formation in MBL, precipitation sink, dry deposition, and advection, respectively. For simplicity, W12 neglected three terms as they are small on average in MBL. W12 estimated dry deposition, |DRY, to be less than 2 cm −3 d −1 and advection, |ADV, to be 10 cm −3 d −1 or less. As for the new particle formation, this term has been set to zero because previous observational studies (e.g., Bates et al., 1998;Covert et al., 1996) suggest that new particle formation in the MBL infrequently occurs and is unlikely to contribute significantly to the mean CCN concentration. Rather, new particle formation appears to occur primarily in the FT (e.g., Humphries et al., 2016;Sanchez et al., 2021) and act as the key source for CCN once they have been brought in the sub-cloud layer and grown to larger, near accumulation-mode sizes (e.g., Covert et al., 1996;Quinn et al., 2017;Raes, 1995). It is nonetheless possible that new particle formation or activation of smaller (Aitken sized) particles may be important over the SO when accumulation mode aerosols are low (I. L. McCoy et al., 2021). Further study is needed on this topic, but for the present study it is neglected. The remaining terms for the FT source, surface source, and precipitation sink were parameterized. W12 derived a steady-state (or equilibrium solution) as N eq for cloud droplet number concentration by setting the time tendency of CCN to zero (i.e., left-hand side of Equation 1) and substituting in the parameterized source and sink terms: where N FT is the FT CCN concentration, z i is the MBL depth, D is the large-scale lower tropospheric divergence, F(σ) is a sea spray source function that depends on the supersaturation (A. D. Clarke et al., 2006), U 10 is the wind speed at 10 m, h is cloud thickness, P CB is the precipitation rate at the cloud base and K is a constant that depends on the collection efficiency (Wood, 2006). Note that here we have modified the power-law relationship in the surface source parametrization from 3.41 10 (as in W12) to 2.8 10 . Recent studies (Hartery et al., 2020;Revell et al., 2019) show that the previous 3.41 10 parametrization (A. D. Clarke et al., 2006;Gong, 2003;Monahan & Muircheartaigh, 1980) can overestimate the surface source by a factor of 2-4 for the SO, while 2.8 10 is a better fit for high-wind environments. Hartery et al. (2020) validated the new 2.8 10 parametrization by comparing the predicted sea spray aerosol concentration with aircraft measurements during SOCRATES. In Section 3, we will compare the budget model results using these two different parameterizations.
In this study, we test the budget model by using SOCRATES observations to calculate N eq and compare it with the observed N d . The SOCRATES campaign took place during January-February 2018 during which the aircraft conducted 15 flights over the SO (McFarquhar et al., 2021). Specifically, we estimate the model inputs (e.g., N FT, P CB, U 10 ) from the aircraft measurements, as described below (more description on the instruments are provided as Text S1 in Supporting Information S1). During SOCRATES, typically, the aircraft flew south at high altitude, descended to just above cloud top before descending through the cloud, and then turning back toward Hobart. During the return flight, cloud and aerosol properties were sampled in situ using a standard flight module ( Figure S1 in Supporting Information S1 is a schematic showing a typical flight module, in situ measurements are available at https://doi.org/10.5065/D6M32TM9). The flight modules consisted of fixed activities such as ramp ascents and descents (sometimes called sawtooths), as well as ∼10 min above-, in-, and below-cloud legs flown at a constant altitude. Our analysis is focused on the below-cloud legs where the cloud-radar and lidar (data are available at https://doi.org/10.5065/D64J0CZS) were pointing upward and could be used to assess precipitation. Specifically, we calculated N eq based on the mean rain rate for the below-cloud legs and other supporting observations from surrounding legs (see Figure S1 in Supporting Information S1 for schematic), as described below, and obtained an associated estimate for observed N d from cloud droplet probe measurements taken in the adjacent in-cloud ramps. The observed cloud are close to adiabatic with little systematic variation in the observed N d with height (Kang et al., 2021).
For FT CCN concentration (N FT ), we use measurements from the Ultra-High-Sensitivity Aerosol Spectrometer (UHSAS; DMT, 2013) during the nearby above-cloud leg. The UHSAS measures the size distribution and concentration of aerosols with diameters between 60 and 1,000 nm. We calculated the concentration of aerosols with diameters larger than 70 nm and discarded 60-70 nm diameter range due to instrument noise (Sanchez et al., 2021). As discussed in Sanchez et al. (2021), the UHSAS concentration above 70 nm diameter have a strong equivalence to the CCN concentration at 0.3% supersaturation.
For the surface source term, we use aircraft-measured wind speed from the below-cloud leg and extrapolate it to 10 m assuming a logarithmic wind profile (Hsu et al., 1994). A value of supersaturation σ = 0.3% is used, which yields a value for F(σ) of 214 m −3 (m s −1 ) −(b−1) (where b is the wind speed exponent 10 ) based on the parameterization of A. D. Clarke et al. (2006). We use 4 mm s −1 for the subsidence rate , which is a typical value for low clouds in the subtropics and mid-latitudes, following I. L. McCoy et al. (2020).
For the precipitation sink term, the cloud thickness (h) is estimated from nearby sawtooth legs, where cloud top and cloud base are defined as the highest and lowest altitude with liquid water content (LWC) > 0.03 g m −3 , following Wood et al. (2011). The results of our analysis are not sensitive to reducing this LWC threshold to a lower value (e.g., 0.005 g m −3 as in L. Zhao et al., 2020). In a few cases, multilayer clouds were present and the top and bottom were chosen to span over the levels that were consistent with the radar and lidar boundaries observed during the below cloud leg. We set K = 2.25 m 2 kg −1 , which is a constant that depends on the collection efficiency of cloud droplets by drizzle drops (Wood, 2006). We estimate the liquid precipitation rate at the cloud base (P CB ) based on the radar-lidar technique of O'Connor et al. (2005). This retrieval is run during the below-cloud legs when both the airbone W-band radar and high spectral resolution lidar (HSRL) were pointing upward, and only when the precipitation is identified as liquid phase. The precipitation phase is determined using HSRL measured particle linear depolarization ratio (PLDR) averaged over all levels below the cloud base. This measurement is taken below cloud base rather than at cloud base to prevent multiple scattering from significantly impacting the PLDR. Photons that are single-scattered from spherical droplets generate no PLDR. We interpret values of PLDR < 0.02 in each lidar column to be indicative of liquid precipitation, and PLDR > 0.05 to be ice, with PLDR values in between being mixed or ambiguous. In Section 3.2, we define each below-cloud leg as a "liquid case" if 10% or less of the lidar columns have a PLDR > 0.05 or as a "mixed-phase case" otherwise.
We assess the fractional contribution of coalescence scavenging to N d by computing the ratio between N eq calculated with and without the precipitation sink, which is simply: (3)

Evaluating the N d Budget Model Accuracy
To quantify the accuracy of the budget model, we apply the model to in situ observations from SOCRATES flights as described in Section 2. Figure 1a shows a comparison of observed N d and model predicted equilibrium values (N eq ) with all the source and sink terms and the adjusted wind speed parametrization as in Equation 2. Each point represents a below-cloud leg sample that had sufficient supporting observations from surrounding legs for the model to be applied. (The aircraft-derived inputs for each sample are given in Table S1 in Supporting Information S1, with corresponding statistics also given in Table S2 in Supporting Information S1). Circular symbols are cases dominated by liquid precipitation while diamond-shaped symbols are mixed-phase cases (as determined from the lidar PLDR, see Section 2). Implications of precipitation phase in the budget model results will be discussed in the next section.
Considering all cases together (Figure 1), we find the budget model performs remarkably well with a correlation coefficient of 0.72 (reported at 95% confidence here and throughout the study). Bias is also quite low, where observed N d is 101 cm −3 while predicted N eq is 106 cm −3 . This level of performance with a low bias and a correlation coefficient ∼0.7 is comparable to the performance of satellite retrievals for N d (Kang et al., 2021). This confirms that the budget model, which has been previously applied over the sub-tropics (W12; Mohrmann et al., 2018;Zheng et al., 2018), can be used with confidence in the mid-latitudes once the wind speed parameterization in the surface term is appropriately adjusted. We will return to the topic of the wind speed and surface contribution to CCN in Section 3.3.

Sensitivity of the Budget Model to Precipitation Phase
We hypothesize that CCN scavenging in SO clouds is dominated by liquid phase processes (i.e., coalescence scavenging). In general, ice precipitation that is driven by vapor deposition will not remove CCN from the atmosphere very efficiently (as one ice crystal may consume as little as one CCN particle if it grows exclusively by vapor deposition after a cloud droplet freezes) and it is only through riming, and to a lesser degree ice-aggregation, that ice precipitation might be expected to contribute significantly to CCN removal (Baltensperger et al., 1998;Garrett et al., 2010). Rimed ice was frequently observed during SOCRATES and in past SO experiments, and secondary ice production through rime-splintering appears to be a significant factor in generating ice precipitation in SO clouds (Huang et al., 2017;McFarquhar et al., 2021;Wang et al., 2020). While rime-scavenging has long been recognized for its impact on the chemical composition of snow (Mitchell & Lamb, 1989) and in recent years on its possible role in controlling black carbon in the Arctic (Flanner et al., 2012;Hegg et al., 2011;Qi et al., 2017;Xu et al., 2019), there has been little, if any, attention paid to the effect of riming on the overall CCN budget in mixed-phase clouds.
To test our hypothesis, Figure 1a compares N eq to observed N d separately for mixed-phase cases (diamonds) and liquid-phase cases (circles). For mixed-phase cases, we use the retrieved precipitation ONLY from lidar and radar columns with liquid precipitation. Specifically, we do not retrieve the precipitation rate during periods when lidar PLDR indicates ice is present, but rather we assume that the coalescence scavenging rate in the columns with ice precipitation is the same as in nearby liquid columns. In the context of the budget model we simply assign to the ice-columns the mean precipitation rate retrieved for the liquid-columns. We have not adjusted the budget model to include a rime-scavenging component. In general, we find that the mixed-phase cases behave similarly to the liquid cases (Figure 1a, Table S2 in Supporting Information S1). For liquid cases, we find a correlation coefficient Black diamonds are the cases associated with mixed-phase precipitation, and, for these cases, the mean retrieved rain rates from the liquid-columns is used for the ice-columns. Black hyphens marked the cases with mean rain rate >0.001 mm hr −1 .
of 0.72 and little bias (mean N eq of 97 vs. mean N d of 96 cm −3 ), while for mixed-phase cases we find a correlation coefficient of 0.7 and slightly more bias (mean N eq of 126 vs. mean N d of 113 cm −3 ). Our phase comparison results imply that CCN scavenging in SO clouds is likely dominated by liquid phase coalescence scavenging and the influence of mixed-phase processes on scavenging is small, at least in low-altitude SO cloud.

Quantifying the Relative Importance of Sources and Sinks
How important is coalescence scavenging in controlling N d ?
We can easily answer this question in the context of the budget model. If the precipitation sink is removed from the model (Figure 1b), the predicted N eq increases substantially, with the mean N eq of liquid cases jumping from 97 ( Figure 1a) to 133 cm −3 (Figure 1b). Figure 2 shows the ratio between N eq calculated with and without coalescence scavenging (Equation 3) as a function of precipitation rate at cloud base. For precipitation rates below about 0.001 mm hr −1 there is no appreciable reduction in N eq . In Figure 1, cases with a precipitation rate greater than 0.001 mm hr −1 are marked with black hyphens. The clear symbols (with no hyphen) remain clustered near but below the one-to-one line in Figure 1b, suggesting that source terms may be a bit too weak. On the other hand, for cases with precipitation rates above 0.001 mm hr −1 , there is a sharp reduction in N eq such that when precipitation rates reach 0.1 mm hr −1 , N eq is reduced to about 10% of what it would have been without precipitation (Figure 2). This result demonstrates that light precipitation with rates <0.1 mm hr −1 significantly impacts CCN and N d . The RF13 cases (pink points in Figures 1 and 2) provide an excellent demonstration of the importance of coalescence scavenging. Measurements during RF13 were collected across a Pocket of Open Cells (POC), that is a region of open-cell or broken stratocumulus surrounded by closed-cell or overcast stratocumulus (see Figure  S2 in Supporting Information S1). POCs are commonly observed in sub-tropical stratocumulus but also occur in SO stratocumulus. Measurement campaigns such as VOCALS have highlighted the importance of precipitation for forming and maintaining these structures (Berner et al., 2011). Not surprisingly, we find that SO POCs are also associated with increased precipitation and lower N d . During RF13, samples in the closed cellular clouds had large values of N d (up to ∼160 cm −3 ) while the two samples in the open cellular cloud regions had much lower values of N d (∼8 and ∼44 cm −3 ), despite having very similar aerosols in the FT and similar surface winds.
What is the relative importance of the FT and surface sources of CCN? Again, we can examine this question in the context of the budget model by neglecting the source terms in estimating N eq . Comparing Figure 1c (no FT source) and Figure 1d (no surface source) suggests that entrainment of FT CCN is playing a larger role than surface sources in controlling N d on average during SOCRATES. For liquid cases, when removing surface sources ( Figure 1d) the mean predicted N eq drops from 97 to 74 cm −3 , while removing FT sources (Figure 1c) reduces N eq to 23 cm −3 . This broadly matches the dominance of sulfur-based accumulation mode aerosols over sea-spray aerosols in the MBL during SOCRATES . Of course, the relative importance of the surface source varies with wind in Figure 1c, with those flights having higher wind speeds (e.g., RF05, RF08, RF12) having the largest N eq . Regardless, our analysis confirms that the FT is a larger source of CCN than the surface over the SO in summer, an idea or hypothesis that has been advanced in previous studies based on surface measurements (Covert et al., 1996;Quinn et al., 2017;Raes, 1995). This differs, however, from the SO result in W12 where the budget model was originally introduced. W12 estimated the ratio of the CCN flux from the surface source to that from the FT and found that in the subtropics and tropics CCN was dominated by the FT source, but the mid-latitudes (including the SO), where winds are stronger, CCN was instead dominated by the surface source. The discrepancy between our analysis and W12 is due to the difference in the surface source parametrization. As noted in Section 2, we have modified the power-law relationship in the surface source parametrization to one that is better suited to the SO. If we use the original budget model (W12) for SOCRATES cases, the predicted N eq is overestimated ( Figure S3 in Supporting Information S1), with the mean N eq (223 cm −3 ) of all cases more than twice of the observed mean N d (101 cm −3 ). This significant bias is caused by the high wind cases when using the original parameterization, as can be seen by examining the difference between N eq and N d as a function of wind speed ( Figure S4 in Supporting Information S1). This highlights the importance of using Figure 2. The ratio between calculated N eq with and without the precipitation sink (Equation 3) as a function of precipitation rate at cloud base. Different colors represent different flights. Black hyphens marked the cases with rain rate >0.001 mm hr −1 (which are to the right of the dashed reference line). Circular points are cases associated with liquid precipitation. Black diamonds are the cases associated with ice precipitation, and, for these cases, retrieved rain rates from liquid columns are used in the budget model. Gray dotted lines are the reference lines calculated using Equation 3 assuming cloud depth h = 100, 400, and 1,000 m. The average cloud depth is about 402 ± 278 m. a good parameterization for the surface source of CCN in the budget model and supports the 2.8 10 relationship obtained by Revell et al. (2019) and Hartery et al. (2020) for the SO.
We also tested the performance of the budget model by using different input data for the surface wind speed and the precipitation rates. Specifically, we used ERA5 wind speed at 10 m (U10 ERA-5 ) as input, keeping all other inputs the same, and found the predicted N eq still showed good agreement with observed N d ( Figure S5a in Supporting Information S1). U10 ERA-5 is highly correlated with the U10 derived from aircraft measurements with a correlation coefficient of 0.96 and little bias (mean U10 ERA-5 of 10.2 m s −1 vs. mean U10 airfract of 9.5 m s −1 ). To examine the sensitivity of the budget model to precipitation rate estimates, we instead used a cloud-base precipitation rate estimated from a radar reflectivity to rain rate (Z-R) relationship developed by Comstock et al. (2004). For liquid cases, the predicted N eq shows good agreement with observed N d ( Figure S5b in Supporting Information S1). We note that for liquid cases the Comstock Z-R relationship was developed for sub-tropical clouds but compares reasonably well with our radar-lidar retrieval-based rain rate estimate ( Figure S6 in Supporting Information S1).

Conclusions
In this study, we present an evaluation of the simple source-and-sink budget model developed in W12 by testing its accuracy with aircraft-based observations during the SOCRATES. The aircraft observations are used to estimate inputs to the budget model: the FT CCN concentration, near-surface wind speed, and cloud-base precipitation rate. We find that the budget model, after the CCN source term is adjusted to better represent SO sea spray aerosols, predicts SO N d with little bias and a correlation coefficient of about 0.7. SOCRATES flights sampled in regimes where liquid-only and mixed-phase precipitation were present. We find that the budget model, when using only the liquid contribution to the precipitation rate (to estimate the coalescence scavenging rate), is able to predict N d for both liquid and mixed-phase cases. This suggests that rime scavenging may not be very important to the SO CCN budget. However, it is important to recall that the SOCRATES data is a small sample of cases that are potentially biased toward cases with less riming. This is due to the experimental setup: sampling took place in the summer, with less ice presence (Danker et al., 2021), and the aircraft actively avoided stratocumulus with large amounts of supercooled liquid drizzle for safety. Thus, further investigation on the importance of rime scavenging seems warranted, especially over the SO during winter when there is more ice and (likely) less liquid water present, and CCN will generally be lower due to a reduction in contributions from biological sources.
The only sink of CCN included in the budget model is coalescence scavenging, which we find reduces the predicted N d by as much as 90% depending on the precipitation rate ( Figure 2). This highlights the importance of coalescence scavenging in controlling CCN and N d . In particular, the results demonstrate that light precipitation with rates <0.1 mm hr −1 significantly impacts CCN number. Such light precipitation is commonplace in SO stratocumulus but these rates are not captured well in current CloudSat W-band radar retrievals (Tansey et al., 2022), making it difficult to derive scavenging rates with CloudSat. This furthur suggests the impact of coalescence scavenging could be larger than the previous estimates based on CloudSat retrievals (I. L. McCoy et al., 2020). In climate models, as well, light precipitation remains poorly (typically over) simulated (e.g., Stephens et al., 2010;Zhou et al., 2021), and is known to have a disproportionately large effect on the aerosols (Wang et al., 2021). How well climate models simulate coalescence scavenging over the SO is an open question, and continued and improved observations of aerosol, cloud and precipitation properties over the SO is needed.
Regarding aerosol sources, we find that overall entrainment of FT CCN plays a larger role than surface sources in controlling N d during SOCRATES. It should be stressed that SO CCN concentrations are much higher in summer (when SOCRATES was held) associated with increased emissions from ocean biology compared to winter (e.g., Ayers & Gras, 1991). This mostly influences the FT CCN source in the budget model as particles are generated from biological emissions above cloud and brought into the BL where they act as the key CCN source (e.g., Raes, 1995). During SOCRATES, the surface contribution is non-negligible for cases associated with high wind speeds. This could reflect increased production of sea spray particles from wind-driven processes (e.g., Grythe et al., 2014), increased fluxes of biological gases that help to grow already present particles to CCN sizes (e.g., Bates et al., 1998), or even an increased entrainment of FT Aitken particles to grow into CCN (e.g., Ayers et al., 1997). Budget model overestimation of N d for these high-wind speed cases was reduced by modifying the 8 of 10 surface source parametrization to a more appropriate SO representation. This, as in the global climate model study by Revell et al. (2019), highlights the importance of using a region appropriate parametrization for windspeed driven surface CCN sources. If this budget model is to be applied widely, a more generalized parameterization may need to be implemented.
Lastly, while the source-sink framework shows skill in capturing observed SO N d variability, there is still room for improvement. One likely source of remaining error is the parameterization of CCN entrainment into the BL. This is currently based on the large-scale divergence and was set to a fixed value. Variability in entrainment may be responsible for much of the remaining discrepancies between observed and predicted N d . Likewise, new particle formation and the role of Aitken mode particles in buffering against precipitation removal of N d and CCN (e.g., I. L. McCoy et al., 2021) is not included in the model. In our view, more detailed examinations of these factors, through large-eddy scale simulations of SOCRATES cases, should be undertaken.

Data Availability Statement
All the data used in this study were downloaded from UCAR/NCAR Earth Observing Laboratory data archive including: low rate flight-level data version 1.3 that are avaliable at UCAR/NCAR-Earth Observing Laboratory (2019, https://doi.org/10.5065/D6M32TM9) and NCAR Cloud Radar and High Spectral Resolution Lidar moments version 2 that are avaliable at NCAR/EOL Remote Sensing Facility (2022, https://doi.org/10.5065/ D64J0CZS).